Abstract
We present a new convergence result for the cone partitioning algorithm with a pure ω-subdivision strategy, for the minimization of a quasiconcave function over a polytope. It is shown that the algorithm is finite when ε-optimal solution with ε > 0 are looked for, and that any cluster point of the points generated by the algorithm is an optimal solution in the case ε = 0. This result improves on the one given previously by the authors, its proof is simpler and relies more directly on a new class of hyperplanes and its associated simplicial lower bound.
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Jaumard, B., Meyer, C. A Simplified Convergence Proof for the Cone Partitioning Algorithm. Journal of Global Optimization 13, 407–416 (1998). https://doi.org/10.1023/A:1008325507949
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DOI: https://doi.org/10.1023/A:1008325507949